I don't think there is universally agreed concept of quantifier for
algebra. Carrying over quantifiers from logic, one may suggest that
summation (http://en.wikipedia.org/wiki/Summation), product, infimum,
and supremum are quantifiers (they are essentially generalizations of
binary operations: addition, multiplication, meet, and join,
correspondingly). It is common in algebra to represent qunatified
operation in terms of binary ones; example:

where D(y) is domain of y (which we assumed earlier to be
{1,2,3,...}). The last expression evaluates to projection which is
well known fact, but misses the big idea that universal and
existential quantifiers are dual quantifiers. Logical quantifiers in
algebraic form are set joins (which in some cases evaluate to
projection and relational division).
Received on Fri Nov 06 2009 - 23:00:24 CET